Quantifying higher-order epistasis: beware the chimera.

Epistasis, or interactions in which alleles at one locus modify the fitness effects of alleles at other loci, plays a fundamental role in genetics, protein evolution, and many other areas of biology. Epistasis is typically quantified by computing the deviation from the expected fitness under an additive or multiplicative model using one of several formulae. However, these formulae are not all equivalent. Importantly, one widely used formula - which we call the chimeric formula - measures deviations from a multiplicative fitness model on an additive scale, thus mixing two measurement scales. We show that for pairwise interactions, the chimeric formula yields a different magnitude, but the same sign (synergistic vs. antagonistic) of epistasis compared to the multiplicative formula that measures both fitness and deviations on a multiplicative scale. However, for higher-order interactions, we show that the chimeric formula can have both different magnitude and sign compared to the multiplicative formula - thus confusing negative epistatic interactions with positive interactions, and vice versa. We resolve these inconsistencies by deriving fundamental connections between the different epistasis formulae and the parameters of the multivariate Bernoulli distribution . Our results demonstrate that the additive and multiplicative epistasis formulae are more mathematically sound than the chimeric formula. Moreover, we demonstrate that the mathematical issues with the chimeric epistasis formula lead to markedly different biological interpretations of real data. Analyzing multi-gene knockout data in yeast, multi-way drug interactions in E. coli , and deep mutational scanning (DMS) of several proteins, we find that 10 - 60% of higher-order interactions have a change in sign with the multiplicative or additive epistasis formula. These sign changes result in qualitatively different findings on functional divergence in the yeast genome, synergistic vs. antagonistic drug interactions, and and epistasis between protein mutations. In particular, in the yeast data, the more appropriate multiplicative formula identifies nearly 500 additional negative three-way interactions, thus extending the trigenic interaction network by 25%.

HATCHet2: clone- and haplotype-specific copy number inference from bulk tumor sequencing data.

Bulk DNA sequencing of multiple samples from the same tumor is becoming common, yet most methods to infer copy-number aberrations (CNAs) from this data analyze individual samples independently. We introduce HATCHet2, an algorithm to identify haplotype- and clone-specific CNAs simultaneously from multiple bulk samples. HATCHet2 extends the earlier HATCHet method by improving identification of focal CNAs and introducing a novel statistic, the minor haplotype B-allele frequency (mhBAF), that enables identification of mirrored-subclonal CNAs. We demonstrate HATCHet2's improved accuracy using simulations and a single-cell sequencing dataset. HATCHet2 analysis of 10 prostate cancer patients reveals previously unreported mirrored-subclonal CNAs affecting cancer genes.